A Generalized Newton-Raphson Method Using Curvature

Communications in Numerical Methods in Engineering, Wiley, Vol 11, pp.757-763, 1995

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Departments of Civil and Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, Taejon 305-701, Korea

Abstract
A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton-Raphson method. The compared results between the proposed method and the Newton- Raphson method are listed. The proposed method has a wider convergent region of initial points and finds more proper solutions than the Newton-Raphson method. In particular, the paper proposes that the curvature method is replaced by the modified Newton method discussed by Ralston in dealing with multiple roots.